How Is Error Possible In Mathematics?

If We Knew Exactly The Laws Of Nature And The Situation Of The Universe At The Initial Moment, We Could Predict Exactly The Situation Of The Same Universe At A Succeeding Moment.

There Are No Solved Problems; There Are Only Problems That Are More Or Less Solved.

Mathematical Discoveries, Small Or Great Are Never Born Of Spontaneous Generation They Always Presuppose A Soil Seeded With Preliminary Knowledge And Well Prepared By Labour, Both Conscious And Subconscious.

The Mathematical Facts Worthy Of Being Studied Are Those Which, By Their Analogy With Other Facts, Are Capable Of Leading Us To The Knowledge Of A Physical Law. They Reveal The Kinship Between Other Facts, Long Known, But Wrongly Believed To Be Strangers To One Another.

Mathematics Has A Threefold Purpose. It Must Provide An Instrument For The Study Of Nature. But This Is Not All: It Has A Philosophical Purpose, And, I Daresay, An Aesthetic Purpose.